Shear Strength Reduction Approach for Slope Stability Analyses

More documents

Recommendations

Info

$Fayek & Kyser 2000 uraninite fractionations.pdf - Queen's University$

In the supported case, however, the results differin terms of the location of the minimum FS ( =SRF), although the Factor of Safety for this newfailure zone falls within the range calculated for thiszone in LEM (FS=1.5 to 1.6). The main difference isthat the LEM still locates the minimum surface(FS=1.37-1.46) through the support as in Figure 11.In addition, the lower right plot in Figure 12 illustratesthat the generation of axial load in the supportsis not constant and does not reach the maximumcapacity. The axial (and shear) load developsas the slope deforms. This is more physically accuratethan the assumption of static full capacity (oreven factored nominal capacity) in LEM analysis.In this analysis, however, the capacity of the boltsare not factored along with soil shear strength in theSSR process. There is, at present, no consensus onwhether they should be (i.e. apply the same SSR tobolt capacity) or how the actual loads in the boltsshould be compared with the bolt capacities to givean FS for the bolts. This is a discussion that isneeded in order to adopt a standard approach forsupported slopes. It is possible to use the SSR approachin a different way and discretely select limitingSRF (for short and long term stability for example)according to accepted practice. This would becompatible with the factored load approach formerging structural and geotechnical engineering.The bolts could then be scaled to provide stabilityfor the strength-reduced slip surface within a structural(steel code) safety margin. This is just one suggestion.It is clear, however, that more discussion iswarranted on the incorporation of support in SSRmodels. Accepting that SSR is mechanically correct,the accounting process for support needs to be furtherdiscussed in the learned community.2.5 Example 5: Stiffness and Strain SofteningThe examples in the previous section were selectedto demonstrate the compatibility of LEM and FEM-SSR techniques for simple slope problems. In eachcase the conditions are fixed and the units are of uniformand high stiffness (the correct approach to obtaindirect comparison between the two methods).The following example explores the effect of multiplematerials, stiffness, strain softening and sensitivitiesto convergence tolerance and mesh density.The layer properties (according to Hoek et al. 2002)for the example in Figure 13 are given in Table 7.Table 7. Strength parameters of the materials in Example 5.UCSMPaUCSresidm i GSI m b s E rmGPaSSt 60 12 21 70 7.2 0.036 16.5Sh1SiltSh215251015251081076065501.92.91.20.0120.0200.0043.09.42.0SSt =Sandstone, Silt =Siltstone, Sh1=shale, Sh2 =weak shaleFigure 13 shows the minimum FS calculated forthree selected LEM solutions using peak and residualstrength parameters for each layer. In this example,the residual strength is specified by reducing thenormalizing UCS. The slope crest is 205m above thelake level.Figure 13: LEM analysis (FS values shown) for a stratifiedrock slope. Left analysis uses peak strength from Table 7;Right analysis uses “resid” strength for the Sandstone.Figure 14 compares the FEM-SSR results formodels with elastic-plastic response (using “peak”parameters from Table 7) using identical elasticproperties and variable (true) elastic properties. Theeffect of stiffness contrasts in this case is not particularlysignificant although there is no reason notto include stiffness variation in an FEM-SSR analysis.The results in either case compare best to thenon-circular Bishop analysis in Figure 13.Figure 14: FEM-SSR analysis of slope in Fig. 13 and Table 7.Shear strain contours and displacement vectors (x25) plotted.Figure 15 shows the SSR results for an analysiswith strain weakening (brittle) behaviour prescribedfor the sandstone. Other lithologies are plastic. SSRis applied to both peak and residual parameters inthis case.Figure 15: FEM-SSR analysis for Example 5 with strain weakeningbehaviour for the sandstone (zero dilation). Water tableis solid line (1). Shear strain (contours) and displacement vectors(x25) are plotted. Note bimodal failure (2 blocks).Proceedings of the 1st Canada-US Rock Mech. Symposium - Vancouver 2007: Invited Session Keynote Paper
Interestingly, the FS (=SRF=1.85) for this analysisis within the range of the LEM analyses for residualparameters. In addition, close examination ofFigure 15 shows that both the non-circular, deepseatedslip surface as well as the shallower circularsurface suggested by alternate LEM analyses (rightside of Figure 13) are both simulated in the FEManalysis (two distinct zones of elevated shear strain).The results shown are for zero-dilation. Failure geometryis similar for dilation (m dil = 0.25m b ) with anelevated FS=SRF=1.92. Table 8 summarizes the impactof mesh density and convergence tolerance.Beyond a reasonable minimum element density, theresults are not very sensitive to mesh configurationalthough poor results are obtained with an elevatedtolerance or the use of 3-noded triangular elements(as opposed to 6-noded linear strain elements).Table 8: Effects of tolerance, maximum iterations per cycleand mesh density for Example 5 with brittle sandstone (Figure15) and zero dilation.Mesh Tolerance Max Iterations FS=SRF(*6 nodes)*Standard 0.001 500 1.85*Standard 0.01 250 2.05*Standard 0.0001 1000 1.82*Coarse (x 0.5) 0.001 500 1.86*Fine (x 2) 0.001 500 1.823 node (stand) 0.001 500 2.033 DISCRETE / DISCONTINUOUS MODELSThe application of SSR is not restricted to continuummodels such as finite element or finite differencetools. This section presents two examples ofapplication in discontinuum analysis.3.1 SSR in Discrete Element AnalysisWhile the equilibrium calculation is based on agroup of slices, limit equilibrium techniques stillconsider the behaviour of a contiguous block of rockor soil in a state of limiting sliding instability. Inmulti-block applications, the development of severalunstable blocks and limited movement does notimmediately indicate failure in an operational sense.The example in Figure 16 illustrates the use of SSRfor a blocky rockmass. The model is created using3DEC and the characterization technique describedby Kalenchuk et al. (2006). A vertical slope is usedfor this simple example. In this model the “actual”joint shear strength properties are specified (cohesoin= 90 kPa, friction angle = 56 deg) although theinitial conditions could be variable and joint specific.The boundary conditions shown are unrealisticand for demonstration only. Failure must be definedand could be based on critical displacement or, as inthis case, a limit for released blocks or cumulativereleased block volume as shown in Figure 17.Figure 16: Schematic 3DEC block models used in Figure 17.Figure 17: Results of SSR analysis for composite model in Figure16. Vertical lines bound the range of FS (=SRF) based ontwo possible failure criteria (see axes). Each point is averagedover several stochastic simulations.3.2 SSR in Discontinuous Deformation AnalysisOne of the fundamental premises of the SSR techniqueis that the factor of safety for any problem canbe related to the factoring of shear strength for materialsand interfaces. Numerous verification examplesillustrate that this gives the same result as an overallforce and moment comparison for sliding problems.It is less clear whether the SSR technique is valid forproblems that do not have a single sliding surfaceand which have internal separation and/or vorticity.The example in Figure 18 demonstrates the applicationof SSR to a simple toppling problem.Figure 18: Example of SSR applied to toppling analysis usingDiscontinuous Deformation Analysis. Critical SRF for interblockfriction and cohesion for this analysis is 1.24. The nominalfriction angle is 30 degrees and the cohesion is 5kPa.Proceedings of the 1st Canada-US Rock Mech. Symposium - Vancouver 2007: Invited Session Keynote Paper
Page 1 and 2: Shear Strength Reduction Approach f
Page 3: einforcement loadings, or shear str

Shear Strength Reduction Approach for Slope Stability Analyses

Create successful ePaper yourself

Delete template?

Save as template?